The former Arsenal and France midfielder leaves New York City FC after a two-and-half year spell in charge of the MLS side.
He returns to Ligue 1 23 years after leaving Cannes to join Milan in 1995.
Vieira, 41, will be joined in Nice by his assistant Christian Lattanzio and members of the New York backroom staff including performance coach Kristian Wilson and physical performance coach Matt Cook.
He is due to be unveiled at a media conference at 2pm (BST) on Monday.
“I would like to thank City Football Group and New York City FC for the opportunity to have coached this tremendous football club. Leaving New York is an incredibly difficult decision for me and for my family and one that has not been taken lightly,” said Vieira
“From the beginning, City Football Group and its leadership, particularly our Chairman Khaldoon Al Mubarak, Brian Marwood, Ferran Soriano and Marty Edelman have believed in me and have helped guide me through the last eight years of my career – starting with my time as a player and ultimately culminating with my first opportunity to manage a First Team.”